How to Convert a Decimal to a Fraction

To convert a terminating decimal to a fraction, write the digits after the decimal point over the matching power of ten, then divide both numbers by their greatest common divisor. For example, 0.75 is 75 over 100, and dividing both by 25 gives 3/4. Every decimal that ends can be converted exactly this way, no guessing and no rounding.

The reason it works is that decimal notation already is a fraction. When you write 0.75 you are saying "75 hundredths". The only work left is reducing that to lowest terms. If you want the answer without doing the arithmetic, the fraction calculator has a Decimal to fraction mode that does both steps and shows the mixed number too.

The Three Steps

1. Count the decimal places. 0.75 has two, so the denominator is 10 to the power of 2, which is 100.
2. Write the digits over that power of ten. Drop the decimal point and use the whole string of digits: 75/100.
3. Reduce by the greatest common divisor. The greatest common divisor of 75 and 100 is 25, so the fraction becomes 3/4.

That is the entire method. Steps 1 and 2 are mechanical. Step 3 is where the answer becomes readable.

Worked Examples

0.75 becomes 3/4

Two decimal places, so 75/100. The greatest common divisor of 75 and 100 is 25. Divide both: 3/4.

0.078125 becomes 5/64

Six decimal places, so 78125/1000000. That looks unpromising, but the greatest common divisor of 78125 and 1000000 is 15625. Divide both and you get 5/64 exactly. This is a good example of why reducing matters: the unreduced form tells you nothing, and the reduced form tells you immediately that the value is five sixty fourths, a number that shows up constantly in binary and in imperial measurement.

2.5 becomes 5/2, or 2 1/2

Handle the whole number and the decimal part together. 2.5 has one decimal place, so it is 25/10, which reduces to 5/2. Because the numerator is larger than the denominator, this is an improper fraction, and it can also be written as the mixed number 2 1/2. Both forms are correct; use whichever your context expects.

0.125 becomes 1/8

Three decimal places gives 125/1000. The greatest common divisor is 125, leaving 1/8.

0.6 becomes 3/5

One decimal place gives 6/10, and the greatest common divisor of 6 and 10 is 2, leaving 3/5.

A Shortcut Worth Memorizing

Any decimal ending in 5 with a denominator that is a power of ten will reduce, because both the numerator and 10 to that power share a factor of 5. More usefully, decimals whose digits are powers of two over powers of two (0.5, 0.25, 0.125, 0.0625, 0.03125, 0.015625, 0.078125) always land on a clean denominator of 2, 4, 8, 16, 32, 64, and so on. If you recognize one of those, you can often write the fraction on sight.

What About Repeating Decimals?

A repeating decimal such as 0.3333... never terminates, so the power of ten method does not finish. The standard algebraic trick is to multiply by 10 and subtract:

x       = 0.3333...
10x     = 3.3333...
10x - x = 3
9x      = 3
x       = 3/9 = 1/3

The same setup handles longer repeats. For 0.121212... you multiply by 100 instead, because two digits repeat, giving 99x = 12 and therefore x = 12/99, which reduces to 4/33.

In practice you rarely type infinite digits. If you enter a truncated repeating decimal such as 0.3333333333333, a calculator cannot know you meant one third, so it returns the closest simple fraction and should tell you the result is an approximation rather than an exact conversion.

Common Mistakes

Forgetting to reduce. 75/100 is a correct answer to "0.75 as a fraction" but almost never the expected one. Reduce unless you were explicitly asked not to.

Miscounting decimal places. The denominator is 10 raised to the number of digits after the point, not the number of digits total. 0.078125 has six digits after the point, so the denominator is 1000000, not 100000.

Dropping the whole number. For 2.5, the answer is 5/2 or 2 1/2, not 1/2. Convert the whole thing, or convert the decimal part and add the whole number back.

Treating a rounded decimal as exact. If a number was already rounded to 0.33 before you started, converting gives 33/100, which is a correct conversion of a wrong input. Convert from the most precise value you have.

Related Tools and Guides

• Fraction calculator to simplify a fraction, convert a decimal, or run arithmetic on two fractions
• Ratio calculator for scaling and solving proportions
• Percentage change calculator for increase and decrease between two values